1. Field of the Invention
The present invention relates to an analog amplifier and an analog filter for amplifying an analog signal. More particularly, the present invention relates to a method for controlling the gain and cutoff frequency exponentially in the variable gain amplifier and variable frequency filter that is capable of changing the gain and cutoff frequency.
2. Description of the Related Art
Typically, a digital variable resistor used in an analog amplifier or an analog filter includes one or more segments, each of which connects to a switch, such that the total resistance of the variable resistor is programmed depending on the connection states of the switches by a digital control signal.
FIG. 1 is a diagram illustrating a binary variable resistor programmed according to a digital control signal according to the related art.
Referring to FIG. 1, the binary variable register 100 is composed of a plurality of segments 101 and a plurality of switches 102 respectively interposed between the segments 101. The connection states of the switches 102 between the resistor segments 101 are controlled by N-bit control signals b0 to bN-1. Assuming that the resistance of the smallest unit resistor of the resistor segment 101 is R, the resistances of the resistor segments 101 of the binary variable resistor are set to R, 22R, . . . , 2N-1R. The connection states of the switches 102 are determined according to the N-bit control signal to change the resistance of the entire binary variable resistor 100.
In the case of the binary variable resistor 100 depicted in FIG. 1, the total resistance of the binary variable resistor 100 is determined in proportion to an integer generated by combining N bits of b0 to bN-1 of the control signal. Here, k satisfies (k=b0+21b1+22b2+ . . . +2N-1bN-1, 0≦k≦2N−1). In a case of applying the binary variable resistor 100 to an operational amplifier (not shown) as its input resistor or to a feedback resistor, the gain value is determined in proportion to the input resistor or feedback resistor so as to obtain the gain value proportional to or inversely-proportional to the integer k.
FIG. 2 illustrates relationships among voltage gain of a variable gain amplifier formed with a variable resistor and an operational amplifier, decibel (dB) of the voltage gain, and the control signal k according to the related art. Assuming that the gain obtained in the case that the integer k generated by combining N bits of the control signal is 1, the total gain of the variable gain amplifier increases linearly as k increases (G, 2G, 3G, . . . ).
FIG. 3 is a graph illustrating a relationship between the decibel value of the gain according to the frequency of a normal loss pass filter and the frequency to explain the cutoff frequency according to the related art. The size of most signals existing in nature such as electric wave, sound, and light increases exponentially such that it is advantageous to express the gain and cutoff frequency on a log scale in an analog circuit for the following signal processes. In the case of expressing the gain value on a log scale, the unit of decibel obtained by applying log to the gain and multiplying by 20 (10 in case of voltage) is used in general. A normal filter varies in output gain to input as the frequency value increases, and there are the pass band and stop band. The cutoff frequency (fc) denotes the boundary frequency between the pass band and stop band. In a case of low pass filter, the frequency having the gain value lower by as much as 3 decibels as compared to the gain of the direct current or low frequency of the pass band is defined as fc. As shown in FIG. 3, the gain value in direct current is Adc (dB), and the gain value at the stop frequency fc is Adc−3 (dB), i.e., lower by as much as 3 decibels as compared to the gain value in direct current.
FIG. 4 is a circuit diagram illustrating an amplifier using the variable resistor of FIG. 1 according to the related art.
Referring to FIG. 4, the amplifier 150 is capable of changing the gain and cutoff frequency by adjusting the resistance of the variable resistors 160 and 170. The gain and cutoff frequency of the amplifier of FIG. 4 in direct current are as follows.
      Gain    ⁢          :        ⁢                  ⁢                  R        b                    R        a              ,          ⁢            f      c        ⁢          :        ⁢                  ⁢          1              2        ⁢                                  ⁢        π        ⁢                                  ⁢                  R          b                ⁢        C            
Here, Ra denotes the resistance of the input variable resistor 160, Rb denotes the resistance of the feedback variable resistor 170, and C denotes capacitance of the capacitor 180.
At this time, the following process is performed in order to change the cutoff frequency on the log scale linearly in dB under a predetermined gain value.
The ideal resistance of the feedback variable resistor 170 is calculated to obtain a specific cutoff frequency value and set the value closest to the idle resistance among the resistance values available for the feedback variable resistor 170 to Rb.
The ideal resistance of the input variable resistor 160 is calculated to maintain the gain regularly and set the value closest to the ideal resistance among the resistance values available for the input variable resistor 160 to Ra.
Referring to FIGS. 1, 2, and 4, the resistances of the variable resistors 100, 160, and 170 vary linearly and their cutoff frequencies are inversely proportional to the resistances. Referring to FIG. 2 in which the resistances of the variable resistors 100, 160, and 170 are depicted on a log scale, the resistance values of the variable resistors 100, 160, and 170 vary fast (on a log scale) with a low value of k while they vary slowly (on a log scale) with the high value of k.
In a case where the resistance Rb of the feedback variable resistor is lowered to increase the cutoff frequency, a failing configuration of the value for determining an accurate cutoff frequency may occur. That is, since the accuracy of the change of the cutoff frequency linearly on a log scale is limited by changing the resistance of the feedback variable resistor 170, it is difficult to find the ideal resistance and thus an approximate value is taken. This is the case for the input variable resistor 160 in which it is ideal for the resistance to vary in proportion to that of the feedback variable resistance 170, such that the approximate value rather than logically calculated value is taken, resulting in a problem of variation of the cutoff frequency fc and gain. That is, a significant quantization error occurs.
Also, another problem occurs in the bandwidth of the cutoff frequency. The cutoff frequency varies according to the resistance of the feedback variable resistor 170 such that, although it is easy to obtain the approximate value close to the ideal resistance since the change of cutoff frequency becomes sensitive to the unit resistance variation with the high resistance in the low frequency bandwidth, there is a shortcoming in that it is difficult to obtain the approximate value close to the ideal resistance since the total resistance is low in the high frequency bandwidth.
FIG. 5 is a graph illustrating variation of gain according to frequency in a case of using the amplifier of FIG. 4 according to the related art. Due to the aforementioned causes, although it is necessary to be constant on a log scale, the cutoff frequency shows a difference of intervals and also the gain value which should be maintained constantly varies.
For these reasons, it is difficult to control the variable gain amplifier or filter using the binary variable resistor of the related art and thus there is a need of a variable resistor formed in a new structure to control the cutoff frequency precisely in high frequency band and to reduce the quantization error.